1. 1-1 Variables and Expressions
You would be wise to listen carefully and take notes! Copy material that is highlighted the same color as the above title.
In this section we are going to learn about mathematical expressions and how to “translate” verbal expressions into mathematical expressions.
Algebra 1A by Gregory Hauca
Glencoe adapted from presentations by Linda Stamper

2. ÷ Pre Quiz 1) increase 1) + 6) 6) plus + 2) 2) decrease −
Write and translate each word into an operation symbol.
1) increase 1) + 6)
6) plus + 2)
2) decrease −
7) difference 7) − 3)
3) more than + 8)
8) quotient ÷ 4)
4) less than −
9) sum 9) + 5)
5) product x
10) times
10) x
Write and answer the following problems.

3. In Algebra, an expression is a mathematical phrase that contains operations, numbers, and/or variables..
You can use letters to represent one or more numbers. When a letter is used to represent a value that can change or vary, it is called a variable.
An expression that represents a particular number is called a numerical expression.
Ex ÷ 3
A variable expression consists of numbers, variables and operations.
Ex. 3x2 + 2x - 1
numbers- ex. 2,-3, π
variables – letters ex. a,x,y
operations - addition, subtraction, multiplication
and division +, -, •, ÷

4. Multiplication Symbols
In variable expressions, a raised dot or parentheses are often used to indicate multiplication as the symbol x can be easily mistaken for the variable x. Here are some ways to represent the product of x and y.
Example. the product of x and y
In general, good algebraic form is the xy version!
Examples. 2y, 3xy
In each expression, the quantities being multiplied are called factors, and the result is called the product.

5. A power is a short way of writing a repeating multiplication.
Powers.
Powers consist of a base and an exponent
Example:
exponent 43
base
word description: four to the third power or
four cubed
factored form: 4 • 4 • 4
A power is a short way of writing a repeating multiplication.
evaluated form: 64

6. Ex.1
Ex.1 Express the power 72 in words. Then write the factored form and evaluate it.
1. Write problem. 72
2. Write word description.
seven to the second power
or seven squared
3. Write factored form.
7 • 7
4. Evaluate. 49

7. Writing expressions in exponential or power form.
y • y • y • y
5 • 5 • 5
3x • 3x • 3x • 3x y4 53
(3x)4
Must have parentheses!
Evaluating expressions.
Ex.7
Ex.5
Ex.6
-32
(-3)2
2 • 2 • 2 • 2
5 • 5 • 5
-(3 • 3)
-3 • -3 16
125 -9 9
Remember! An exponent applies only to what is directly in front of it.

8. In English there is a difference between a phrase and a sentence
In English there is a difference between a phrase and a sentence. Sentences have verbs and phrases do not.
Phrases are translated into expressions.
Sentences are translated into equations and inequalities.
Remember! A numeric expression is made up of numbers and operations (ex. 5 – 3).
A variable expression is made up of variables, numbers and operations. (ex x).
In this section we are only going to translate phrases into expressions.

9. Words representing operations.
add
subtract
multiply
divide
plus
minus
times
quotient
sum
difference
product
increased by
decreased by of
total
diminished by
twice
less
more than
less than
added to
subtracted from

10. Translating phrases into variable expressions.
1. The sum of a number and 30
n + 30
greater than a number
n + 11
Note that translation of this phrase “switches” the order of what is read. The expression n would NOT be correct.
3. A number decreased by 75
n – 75
4. a number subtracted from 15
15 – n
5. The product of 5 and a number 5n
The translation of this phrase also “switches” the order of what is read.
6. The product of a number and 4 4n
Not 5·n or 5(n) or (5)(n)
In products of numbers and variables the number is always placed first. Do not write “ n4 ”. n 6
n ÷ 6
7. The quotient of a number and 6
Use a fraction bar in algebra to designate division! Not a ÷ symbol.
The first number is always the numerator (on top)

11. Multiple Operation Phrases
Some phrases require more than one operation or variable when translating them. In some you will need grouping symbols to show the correct order of operations.
1. Twice a number plus 7
2n + 7
2 • n
+ 7
2. 5 more than the product of a number and 4
4n + 5
4 • n
+ 5
3. The difference of 8 and three times a number
8 – 3n
8 -
3 • n
4. A number cubed divided by 2 2

12. Class Practice
Translate:
a number minus 12
n - 12
six times a number 6n
a number divided by 8
the sum of 15 and a number
15 + n
the difference of a number and 6.7
n – 6.7
the quotient of 17 and a number

13. Translate:
15 more than a number
n + 15
the product of a number and 6 6n
not n6
5.2 less than a number
the product of 6 and a number, subtract 10 6n
- 10
the quotient of a number and 10, plus 2
+ 2
twice the sum of a number and 15 2
(n + 15)
the difference of a number and 6, divided by 4
not 2n + 15

14. Homework
HW1–A Pages 8-9 #13-22,26,28,30-33,46.

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16. Whiteboard Practice
Translate:
A number minus 12
n - 12
Translate:
six times a number 6n
Translate:
a number divided by 8

17. Translate:
the sum of 15 and a number
15 + n
Translate:
the difference of a number and 6.7
n – 6.7
Translate:
The quotient of 17 and a number

18. Translate:
15 more than a number
n + 15
Translate:
the product of a number and 6 6n
not n6
Translate:
5.2 less than a number

19. The product of 6 and a number, subtract 10
- 10
The quotient of a number and 10, plus 2
+ 2

20. Twice the sum of a number and 152
(n + 15)
not 2n + 15
The difference of a number and 6, divided by 4

21. Did you use a fraction bar to designate division?
Ex.1.
a. 11 greater than a number
n + 11
b. a number subtracted from 15
15 – n
Did you use a fraction bar to designate division?
c. The sum of a number and 30
n + 30
d. Maria’s age minus 27
a – 27 18 n
e. The quotient of 18 and a number
f. The sum of a number and ten, divided by two.

22. Writing word phrases as algebraic expressions.
a. The difference of a number and 7
n – 7
b. 32 increased by a number
32 + n
Use a fraction bar to designate division!
c. 25 less than a number 25 n –
The number always comes before the variable?
d. The quotient of a number and six. n 6
e. The product of a number and five 5n
f. 10 less the product of 5 and a number cubed
10 – 5n3

23. Remember! Use a fraction bar to designate division?
Ex.1
a. 11 greater than a number
n + 11
b. a number subtracted from 15
15 – n
Remember! Use a fraction bar to designate division?
c. The sum of a number and 30
n + 30
d. Maria’s age minus 27
a – 27 18 n
e. The quotient of 18 and a number
f. The sum of a number and ten, divided by two.

24. Ex.2
a. eight more than a number
n + 8
b. seven less the product of 4 and a number x
7 – 4x
c. n cubed divided by 2
d. 9 more than the quotient of b and 5
e. one third the original area of a
f. thirteen less than a number
n - 13

25. Translating phrases into variable expressions.
Addition phrases :
a. The sum of a number and 30
n + 30
b. 12 plus a number
12 + a
c. 32 increased by a number
32 + x
d. 11 greater than a number
p + 11
e. 7 more than a number
y + 7
Note that translation of this phrase “switches” the order of what is read. The expression p would NOT be correct.
The translation of this phrase also “switches” the order of what is read. The word “than” often indicates you may need to switch.

26. Subtraction phrases :
a. The difference between a number and 7
n – 7
b. A number minus 27
x – 27
c. A number decreased by 75
a – 75
d. 25 less than a number
y – 25
e. a number subtracted from 15
15 – p
Note that translation of this phrase “switches” the order of what is read. The expression y would NOT be correct.
The translation of this phrase also “switches” the order of what is read.

27. Remember in products the number always comes before the variable.
Multiplication phrases :
a. The product of 5 and a number 5n
Not 5·n or 5(n) or (5)(n)
b. The product of a number and 5 5n
In products of numbers and variables the number is always placed first. Do not write “ n5 ”.
c. Twice a number 2p
d times a number
300x
Twice means 2 times.
e. A number times 7 7a
Remember in products the number always comes before the variable.

28. a. The quotient of a number and 6 n 6 n ÷ 6
Division phrases:
a. The quotient of a number and 6 n 6
n ÷ 6
Use a fraction bar in algebra to designate division! Not a ÷ symbol.
The first number is always the numerator (on top)
b. The quotient of 18 and a number 18 x
c. A number divided by 12 a 12